Abstract

Co-authors: Harald Garcke (University of Regensburg), Michael Hinze (University of Hamburg)

In [Abels, Garcke, Gruen, M3AS , 22, 2012] a model for the simulation of variable density two-phase flow using the diffuse interface approach is presented. Due to an additional transport term in the Navier-Stokes system this model enjoys consistency with thermodynamics. To preserve this important property in the numerical simulation we propose a time discretization that uses a carefully designed weak formulation and delivers a time discrete variant of the continuous energy equality. The spatial discretization is enriched by a suitable post processing step to ensure the energy inequality to hold in the fully discrete setting. An a-posteriori adaptive procedure is proposed that deals with the errors both in the Navier-Stokes and the Cahn-Hilliard system.